2026-27

The Kardar--Parisi--Zhang universality class is a central topic in mathematical physics and probability theory. In this talk, we discuss the conjectural scaling limit of periodic models in the Kardar--Parisi--Zhang universality class: the periodic directed landscape. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape and give a variational characterization of the periodic KPZ fixed point, recently constructed by Baik, Liao, and Liu. We also establish the convergence of periodic asymmetric simple exclusion processes to periodic KPZ fixed points, coupled through the same periodic directed landscape. A key ingredient is a gluing technique for combining overlapping directed landscapes, which may be of independent interest. This is based on joint work with Amol Aggarwal and Ivan Corwin. 

Firstly, the close relations between Complete Positivity (CP) of quantum open system dynamics and quantum entanglement will be discussed.
Secondly, it will be argued that the typicality of entanglement in high dimensional quantum systems might spoil those approaches that consider Complete Positivity an artificial and simplifying mathematical artifact rather than a physically necessary constraint on any quantum dynamics.